Almost-optimal parallel algorithms for exact single-source shortest paths (SSSP) on directed graphs

Develop an almost-optimal parallel algorithm for exact single-source shortest paths on general directed graphs that achieves m^{1+o(1)} work and m^{o(1)} depth in the parallel setting.

Background

The paper introduces DAG projections that reduce the difficulty of exact directed SSSP to easier settings, such as exact SSSP on undirected graphs and (1+1/polylog n)-approximate SSSP on DAGs. These reductions preserve near-optimal parallel work and depth up to subpolynomial factors, sharpening the focus of the open problem to these simpler regimes.

Despite strong approximate and undirected results, an almost-optimal parallel algorithm for exact SSSP on general directed graphs remains elusive; the authors explicitly frame this as a major open problem and show that progress on the reduced settings would resolve it.